Nature of optical excitations in the frustrated kagome compound Herbertsmithite

Optical conductivity measurements are combined with density functional theory calculations in order to understand the electrodynamic response of the frustrated Mott insulators Herbertsmithite $\mathrm{ZnCu_{3}(OH)_{6}Cl_{2}}$ and the closely-related kagome-lattice compound $\mathrm{Y_{3}Cu_{9}(OH)_{19}Cl_{8}}$. We identify these materials as charge-transfer rather than Mott-Hubbard insulators, similar to the high-$T_c$ cuprate parent compounds. The band edge is at 3.3 and 3.6 eV, respectively, establishing the insulating nature of these compounds. Inside the gap, we observe dipole-forbidden local electronic transitions between the Cu $3d$ orbitals in the range 1--2 eV. With the help of \textit{ab initio} calculations we demonstrate that the electrodynamic response in these systems is directly related to the role of on-site Coulomb repulsion: while charge-transfer processes have their origin on transitions between the ligand band and the Cu $3d$ upper Hubbard band, \textit{local} $d$-$d$ excitations remain rather unaffected by correlations.